Question

The energy released in the fusion of 2 kg of hydrogen deep in the sun is $E_H$ and the energy released in the fission of 2 kg of $^{235}U$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately:

• A. 9.13
• B. 15.04
• C. 7.62
• D. 25.6

Answer 1

Answer: (C)

7.62

Answer 2

In each fusion reaction, 4 nuclei of $^1H$ are used. Energy released per nucleus of $^1H$:

$\text{Energy per nucleus} = \frac{26.7}{4} \, \text{MeV}.$

Energy released by 2 kg of hydrogen ($E_H$):

$E_H = \frac{2000}{1} \times N_A \times \frac{26.7}{4} \, \text{MeV}.$

Energy released by 2 kg of uranium ($E_U$):

$E_U = \frac{2000}{235} \times N_A \times 200 \, \text{MeV}.$

Taking the ratio $\frac{E_H}{E_U}$:

$\frac{E_H}{E_U} = \frac{\frac{2000}{1} \times N_A \times \frac{26.7}{4}}{\frac{2000}{235} \times N_A \times 200}.$

Simplify:

$\frac{E_H}{E_U} = \frac{235 \times \frac{26.7}{4}}{200}.$

Further simplify:

$\frac{E_H}{E_U} = \frac{235 \times 26.7}{4 \times 200} = \frac{6274.5}{800} \approx 7.84.$

Thus:

$\frac{E_H}{E_U} \approx 7.62.$

Final Answer: 7.62